论文标题
数字和权力法的基础代表
The base-e representation of numbers and the power law
论文作者
论文摘要
研究了数字最佳表示的某些特性。对基础E的表示形式进行了检查，以编码整数。引入了我们称之为WF的无分数的大概表示，并将其与base-2和Base-3表示形式进行了比较，而base-2和基本3表示效率仅次于基础。由于树木类似于数字表示，因此我们探讨了基本-E系统在理解复杂系统行为和社交网络的统计最优性方面的相关性。我们表明，这为许多开放的复杂系统所表现出的权力法的性质提供了一种新的理论解释。具体而言，我们表明，最常针对此类系统提出的功率定律具有类似于最佳基础-E表示形式的形式。
Some properties of the optimal representation of numbers are investigated. This representation, which is to the base-e, is examined for coding of integers. An approximate representation without fractions that we call WF is introduced and compared with base-2 and base-3 representations, which are next to base-e in efficiency. Since trees are analogous to number representation, we explore the relevance of the statistical optimality of the base-e system for the understanding of complex system behavior and of social networks. We show that this provides a new theoretical explanation for the nature of the power law exhibited by many open complex systems. In specific, we show that the power law distribution most often proposed for such systems has a form that is similar to that derived from the optimal base-e representation.
